A process-independent explanation for the general form of Taylor's Law

Abstract

Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many ecological explanations have been proposed for TL but it is also commonly observed outside ecology. We propose that TL arises from the constraining influence of two primary variables: the number of individuals and the number of censuses or sites. We show that most possible configurations of individuals among censuses or sites produce the power-law form of TL with exponents between 1 and 2. This feasible set approach suggests that TL is a statistical pattern driven by two constraints, providing an a priori explanation for this ubiquitous pattern. However, the exact form of any specific mean-variance relationship cannot be predicted in this way, i.e., this approach does a poor job of predicting variation in the exponent, suggesting that TL may still contain ecological information.